Explanation:
Let x be the first negative odd integer.
Then the next two negative consecutive odd integers are x-2 and x-4.
The problem states that the product of the two smaller integers is 13 less than four times the larger integer. In equation form, this can be written as:
(x-4)(x-2) = 4(x) - 13
Expanding the left side of the equation:
x^2 - 6x + 8 = 4x - 13
Simplifying:
x^2 - 10x + 21 = 0
Factoring the left side of the equation:
(x-7)(x-3) = 0
Therefore, x = 7 or x = 3.
If x = 7, then the three consecutive odd integers are 5, 3, and 1, which are not negative.
If x = 3, then the three consecutive odd integers are 1, -1, and -3.
Therefore, the three negative consecutive odd integers that satisfy the problem are -3, -1, and 1.